$\int z^3\,dz=$ $+C$
The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int z^{{3}}\,dz&=\dfrac{z^{{3}+1}}{{3}+1}+C \\\\ &=\dfrac14 z^4+C \end{aligned}$ In conclusion, $\int z^3\,dz=\dfrac14 z^4+C$